Fall 2015
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.
Date: October 23, 2015
Speaker: George Biros
Institute for Computational Engineering and Sciences,
University of Texas at Austin
Title: "Fast Integral Equation Algorithms for Boundary Value Problems with Variable Coefficients"
Abstract:
Typically, boundary value problems are solved numerically by discretizing the corresponding partial differential equations. However, alternative discretization schemes can be derived by considering integral equation formulations. Integral equation formulations have several advantages. For example, they allow high-order, non-conforming discretizations. They also have disadvantages, with respect their generality, their computational cost, and their steep learning curve. One major challenge with integral equation methods is the evaluation of the so-called volume potentials, that is, volume integrals with weakly singular kernels. The evaluation of such volume integrals is a well understood problem. Volume integral equations can be used for solving boundary value problems, for example the Laplace, Stokes and Helmholtz problems. Despite the significance of such methods, there exist no scalable efficient implementations and as a result their use from non-experts is somewhat limited. I will discuss the formulation, numerical challenges and scalability of algorithms for volume integral equations and I will present a new open-source library for such problems. I will compare their performance to other state-of-the art codes and conclude with an example from computational fluid mechanics.
This is joint work with Dhairya Malhotra.